TSTP Solution File: LCL682+1.001 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL682+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:10:48 EDT 2023
% Result : Theorem 4.25s 4.42s
% Output : Proof 4.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL682+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 19:01:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.25/4.42 SZS status Theorem for theBenchmark.p
% 4.25/4.42 SZS output start Proof for theBenchmark.p
% 4.25/4.42 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), r1 X X) True
% 4.25/4.42 Clause #1 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (r1 X Y) (r1 Y Z) → r1 X Z) True
% 4.25/4.42 Clause #2 (by assumption #[]): Eq
% 4.25/4.42 (Not
% 4.25/4.42 (Not
% 4.25/4.42 (Exists fun X =>
% 4.25/4.42 Not
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Not
% 4.25/4.42 (∀ (Y : Iota),
% 4.25/4.42 Or (Not (r1 X Y))
% 4.25/4.42 (Not
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X)))
% 4.25/4.42 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.42 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X))))
% 4.25/4.42 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p11 X)))))))
% 4.25/4.42 True
% 4.25/4.42 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r1 a a) True
% 4.25/4.42 Clause #4 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (r1 a Y) (r1 Y Z) → r1 a Z) True
% 4.25/4.42 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (r1 a a_1) (r1 a_1 Z) → r1 a Z) True
% 4.25/4.42 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (And (r1 a a_1) (r1 a_1 a_2) → r1 a a_2) True
% 4.25/4.42 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (r1 a a_1) (r1 a_1 a_2)) False) (Eq (r1 a a_2) True)
% 4.25/4.42 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 a a_1) True) (Or (Eq (r1 a a_2) False) (Eq (r1 a_2 a_1) False))
% 4.25/4.42 Clause #11 (by clausification #[2]): Eq
% 4.25/4.42 (Not
% 4.25/4.42 (Exists fun X =>
% 4.25/4.42 Not
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Not
% 4.25/4.42 (∀ (Y : Iota),
% 4.25/4.42 Or (Not (r1 X Y))
% 4.25/4.42 (Not
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X)))
% 4.25/4.42 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.42 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X))))
% 4.25/4.42 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p11 X))))))
% 4.25/4.42 False
% 4.25/4.42 Clause #12 (by clausification #[11]): Eq
% 4.25/4.42 (Exists fun X =>
% 4.25/4.42 Not
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Not
% 4.25/4.42 (∀ (Y : Iota),
% 4.25/4.42 Or (Not (r1 X Y))
% 4.25/4.42 (Not
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X)))
% 4.25/4.42 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.42 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X))))
% 4.25/4.42 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.42 (∀ (Y : Iota), Or (Not (r1 X Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p11 X)))))
% 4.25/4.42 True
% 4.25/4.42 Clause #13 (by clausification #[12]): ∀ (a : Iota),
% 4.25/4.42 Eq
% 4.25/4.42 (Not
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.42 (Or
% 4.25/4.44 (Not
% 4.25/4.44 (∀ (Y : Iota),
% 4.25/4.44 Or (Not (r1 (skS.0 0 a) Y))
% 4.25/4.44 (Not
% 4.25/4.44 (Or
% 4.25/4.44 (Or
% 4.25/4.44 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X)))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X))))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p11 X)))))
% 4.25/4.44 True
% 4.25/4.44 Clause #14 (by clausification #[13]): ∀ (a : Iota),
% 4.25/4.44 Eq
% 4.25/4.44 (Or
% 4.25/4.44 (Or
% 4.25/4.44 (Or
% 4.25/4.44 (Or
% 4.25/4.44 (Not
% 4.25/4.44 (∀ (Y : Iota),
% 4.25/4.44 Or (Not (r1 (skS.0 0 a) Y))
% 4.25/4.44 (Not
% 4.25/4.44 (Or
% 4.25/4.44 (Or
% 4.25/4.44 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X)))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X))))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p11 X))))
% 4.25/4.44 False
% 4.25/4.44 Clause #16 (by clausification #[14]): ∀ (a : Iota),
% 4.25/4.44 Eq
% 4.25/4.44 (Or
% 4.25/4.44 (Or
% 4.25/4.44 (Or
% 4.25/4.44 (Not
% 4.25/4.44 (∀ (Y : Iota),
% 4.25/4.44 Or (Not (r1 (skS.0 0 a) Y))
% 4.25/4.44 (Not
% 4.25/4.44 (Or
% 4.25/4.44 (Or
% 4.25/4.44 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X)))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X))))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.44 False
% 4.25/4.44 Clause #27 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))) False
% 4.25/4.44 Clause #28 (by clausification #[16]): ∀ (a : Iota),
% 4.25/4.44 Eq
% 4.25/4.44 (Or
% 4.25/4.44 (Or
% 4.25/4.44 (Not
% 4.25/4.44 (∀ (Y : Iota),
% 4.25/4.44 Or (Not (r1 (skS.0 0 a) Y))
% 4.25/4.44 (Not
% 4.25/4.44 (Or
% 4.25/4.44 (Or
% 4.25/4.44 (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X))))
% 4.25/4.44 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X))))
% 4.25/4.44 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p13 X))))
% 4.25/4.44 False
% 4.25/4.44 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota),
% 4.25/4.44 Eq (Not (Or (Not (r1 (skS.0 0 a) (skS.0 3 a a_1))) (∀ (X : Iota), Or (Not (r1 (skS.0 3 a a_1) X)) (p12 X)))) True
% 4.25/4.44 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota),
% 4.25/4.44 Eq (Or (Not (r1 (skS.0 0 a) (skS.0 3 a a_1))) (∀ (X : Iota), Or (Not (r1 (skS.0 3 a a_1) X)) (p12 X))) False
% 4.25/4.44 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (X : Iota), Or (Not (r1 (skS.0 3 a a_1) X)) (p12 X)) False
% 4.25/4.44 Clause #32 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Not (r1 (skS.0 0 a) (skS.0 3 a a_1))) False
% 4.25/4.47 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (Not (Or (Not (r1 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) (p12 (skS.0 4 a a_1 a_2)))) True
% 4.25/4.47 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (Or (Not (r1 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) (p12 (skS.0 4 a a_1 a_2))) False
% 4.25/4.47 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (p12 (skS.0 4 a a_1 a_2)) False
% 4.25/4.47 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (Not (r1 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) False
% 4.25/4.47 Clause #37 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a) (skS.0 3 a a_1)) True
% 4.25/4.47 Clause #38 (by superposition #[37, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) True) (Or (Eq True False) (Eq (r1 (skS.0 3 a a_2) a_1) False))
% 4.25/4.47 Clause #41 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True
% 4.25/4.47 Clause #43 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) True) (Eq (r1 (skS.0 3 a a_2) a_1) False)
% 4.25/4.47 Clause #44 (by superposition #[43, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) (skS.0 4 a a_1 a_2)) True) (Eq False True)
% 4.25/4.47 Clause #51 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Eq (r1 (skS.0 0 a) (skS.0 4 a a_1 a_2)) True
% 4.25/4.47 Clause #56 (by clausification #[28]): ∀ (a : Iota),
% 4.25/4.47 Eq
% 4.25/4.47 (Or
% 4.25/4.47 (Not
% 4.25/4.47 (∀ (Y : Iota),
% 4.25/4.47 Or (Not (r1 (skS.0 0 a) Y))
% 4.25/4.47 (Not
% 4.25/4.47 (Or
% 4.25/4.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))))))
% 4.25/4.47 (∀ (Y : Iota), Or (Not (r1 (skS.0 0 a) Y)) (∀ (X : Iota), Or (Not (r1 Y X)) (p15 X))))
% 4.25/4.47 False
% 4.25/4.47 Clause #82 (by clausification #[56]): ∀ (a : Iota),
% 4.25/4.47 Eq
% 4.25/4.47 (Not
% 4.25/4.47 (∀ (Y : Iota),
% 4.25/4.47 Or (Not (r1 (skS.0 0 a) Y))
% 4.25/4.47 (Not
% 4.25/4.47 (Or
% 4.25/4.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X)))))))
% 4.25/4.47 False
% 4.25/4.47 Clause #103 (by clausification #[82]): ∀ (a : Iota),
% 4.25/4.47 Eq
% 4.25/4.47 (∀ (Y : Iota),
% 4.25/4.47 Or (Not (r1 (skS.0 0 a) Y))
% 4.25/4.47 (Not
% 4.25/4.47 (Or
% 4.25/4.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p14 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 Y X)) (p12 X))))))
% 4.25/4.47 True
% 4.25/4.47 Clause #104 (by clausification #[103]): ∀ (a a_1 : Iota),
% 4.25/4.47 Eq
% 4.25/4.47 (Or (Not (r1 (skS.0 0 a) a_1))
% 4.25/4.47 (Not
% 4.25/4.47 (Or
% 4.25/4.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p14 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X))))))
% 4.25/4.47 True
% 4.25/4.47 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota),
% 4.25/4.47 Or (Eq (Not (r1 (skS.0 0 a) a_1)) True)
% 4.25/4.47 (Eq
% 4.25/4.47 (Not
% 4.25/4.47 (Or
% 4.25/4.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p14 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X)))))
% 4.25/4.47 True)
% 4.25/4.47 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota),
% 4.25/4.47 Or
% 4.25/4.47 (Eq
% 4.25/4.47 (Not
% 4.25/4.47 (Or
% 4.25/4.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 a X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 a X)) (p12 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 a X)) (p14 X))))
% 4.25/4.47 (Not (∀ (X : Iota), Or (Not (r1 a X)) (p12 X)))))
% 4.25/4.47 True)
% 4.25/4.47 (Eq (r1 (skS.0 0 a_1) a) False)
% 4.25/4.47 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota),
% 4.25/4.47 Or (Eq (r1 (skS.0 0 a) a_1) False)
% 4.25/4.47 (Eq
% 4.25/4.47 (Or
% 4.25/4.47 (Or (Or (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p16 X))) (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X))))
% 4.25/4.48 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p14 X))))
% 4.25/4.48 (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X))))
% 4.25/4.48 False)
% 4.25/4.48 Clause #108 (by clausification #[107]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Not (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X))) False)
% 4.25/4.48 Clause #110 (by clausification #[108]): ∀ (a a_1 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (∀ (X : Iota), Or (Not (r1 a_1 X)) (p12 X)) True)
% 4.25/4.48 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Eq (Or (Not (r1 a_1 a_2)) (p12 a_2)) True)
% 4.25/4.48 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (Not (r1 a_1 a_2)) True) (Eq (p12 a_2) True))
% 4.25/4.48 Clause #113 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), Or (Eq (r1 (skS.0 0 a) a_1) False) (Or (Eq (p12 a_2) True) (Eq (r1 a_1 a_2) False))
% 4.25/4.48 Clause #122 (by superposition #[113, 3]): ∀ (a a_1 : Iota), Or (Eq (p12 a) True) (Or (Eq (r1 (skS.0 0 a_1) a) False) (Eq False True))
% 4.25/4.48 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), Or (Eq (p12 a) True) (Eq (r1 (skS.0 0 a_1) a) False)
% 4.25/4.48 Clause #127 (by superposition #[123, 51]): ∀ (a a_1 a_2 : Iota), Or (Eq (p12 (skS.0 4 a a_1 a_2)) True) (Eq False True)
% 4.25/4.48 Clause #173 (by clausification #[127]): ∀ (a a_1 a_2 : Iota), Eq (p12 (skS.0 4 a a_1 a_2)) True
% 4.25/4.48 Clause #174 (by superposition #[173, 35]): Eq True False
% 4.25/4.48 Clause #176 (by clausification #[174]): False
% 4.25/4.48 SZS output end Proof for theBenchmark.p
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